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Mark the following either true or false. Justification is required when the statement is false. (a) If A is a 7 x 4 matrix and T is defined by T(x) = Ar, then T cannot be one-to-one. (b) If A is a 7 x 4 matrix and T is defined by T(x) = Ax, then T will not map onto R¹. (c) Every matrix transformation is a linear transformation.

Mark the following either true or false. Justification is required when the statement is false. (a) If A is a 7 x 4 matrix and T is defined by T(x) = Ar, then T cannot be one-to-one. (b) If A is a 7 x 4 matrix and T is defined by T(x) = Ax, then T will not map onto R¹. (c) Every matrix transformation is a linear transformation.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Mark the following either true or false. Justification is required when the statement is false. (a) If A is a 7 x 4 matrix and T is defined by T(x) = Ar, then T cannot be one-to-one. (b) If A is a 7 x 4 matrix and T is defined by T(x) = Ax, then T will not map onto R7. (c) Every matrix transformation is a linear transformation.
Transcribed Image Text:Mark the following either true or false. Justification is required when the statement is false. (a) If A is a 7 x 4 matrix and T is defined by T(x) = Ar, then T cannot be one-to-one. (b) If A is a 7 x 4 matrix and T is defined by T(x) = Ax, then T will not map onto R7. (c) Every matrix transformation is a linear transformation.
Expert Solution
Step 1: Given the information

The given statements,

(a) If A is a 7 cross times 4 matrix and T is defined by T open parentheses x close parentheses equals A x, then T cannot be one-to-one.

(b) If A is a 7 cross times 4 matrix and T is defined by T open parentheses x close parentheses equals A x, then T will not map onto straight real numbers to the power of 7.

(c) Every matrix transformation is a linear transformation.

The aim is to check whether the statements are true or false.

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